 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| M. V. Deryabin and V. V. Kozlov, "On the surfacing effect for a heavy rigid body in a fluid," Mech. Solids. 37 (1), 54-59 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
1 |
Pages |
54-59 |
| Title |
On the surfacing effect for a heavy rigid body in a fluid |
| Author(s) |
M. V. Deryabin (Moscow)
V. V. Kozlov (Moscow) |
| Abstract |
The fall of a heavy rigid body in unbounded volume
of an ideal fluid is considered. The fluid performs an irrotational
motion and rests at infinity. It is assumed that the wider side
of the body is horizontal at the initial time instant at which
a velocity is communicated to the body in the horizontal direction.
Then at the next time instants the body starts descending. However,
if the associated mass of the body in the transverse direction
is sufficiently large, the body then sharply comes to the surface
with his narrower side ahead and rises to the height exceeding that
at the initial time instant. The analysis of the surfacing effect
involves the expansion of the solutions of Kirchhoff's equations into
series in powers of time and the evaluation of the coefficients of these
series by means of Cauchy majorants. |
| References |
| 1. | S. A. Chaplygin, "On the motion of heavy bodies in
an incompressible fluid," in S. A. Chaplygin, Complete
Works [in Russian], Izd-vo AN SSSR, Leningrad, 1933, Vol. 1,
pp. 133-150. |
| 2. | G. Kirchhoff, "Über die Bewegung eines Rotationskorpers
in einer Flussigkeit," J. Reine und
Angewan. Math., Vol. 71, pp. 237-262, 1870. |
| 3. | V. V. Kozlov, "On the fall of a heavy rigid body
in an ideal fluid," Izv. AN SSSR. MTT [Mechanics of Solids],
No. 5, pp. 10-17, 1989. |
| 4. | V. V. Kozlov, "On the stability of equilibria
in an unsteady force field," PMM [Applied Mathematics and Mechanics],
Vol. 55, No. 1, pp. 12-19, 1991. |
| 5. | M. V. Deryabin, "On asymptotics of the solution of Chaplygin
equations," Regular and Chaotic Dynamics, Vol. 3, No. 1, pp. 93-97,
1998. |
| 6. | N. E. Zhukovskii, "On the fall of light-weighted elongated bodies
rotating about their longitudinal axes," in N. E. Zhukovskii, Complete
Works. Volume 5 [in Russian], pp. 72-80, Izd-vo AN SSSR, Moscow,
Leningrad, 1937. |
| 7. | V. V. Golubev, Lectures on the Analytical Theory of Differential
Equations [in Russian], Gostekhizdat, Moscow, Leningrad, 1950. |
| 8. | Yu. I. Neimark and N. A. Fufaev, Dynamics of Nonholonomic Systems
[in Russian], Nauka, Moscow, 1967. |
| 9. | V. I. Arnol'd, V. V. Kozlov, and A. I. Neishtadt,
"Mathematical aspects of the classical and celestial mechanics,"
in Achievements in Science and Technology. Ser. Modern Problems
of Mathematics. Basic Directions. Volume 3 [in Russian], VINITI,
Moscow, 1985. |
| 10. | V. V. Kozlov, "Dynamics of systems with nonintegrable constraints.
I, II," Vestnik MGU [Bulletin of the Moscow State University], Ser. 1,
No. 3, pp. 92-100; No. 4, pp. 70-76, 1982. |
| 11. | G. Zamperi, "Nonholonomic versus vakonomic dynamics,"
J. Differ. Equat., Vol. 163, No. 2, pp. 335-347, 2000. |
|
| Received |
21 September 2000 |
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